Related papers: A coarse invariant for all metric spaces

Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. A cone spherical metric is called irreducible if each developing map of the metric does not have…

We study invariant and bi-invariant metrics on groups focusing on finite groups $G$. We show that non-equivalent (bi) invariant metrics on $G$ are in 1-1 correspondence with unitary symmetric (conjugate) partitions on $G$. To every metric…

In this article, we classify the set of asymptotic mass-like invariants for asymptotically hyperbolic metrics. It turns out that the standard mass is just one example (but probably the most important one) among the two families of…

This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…

The monopole map defines an element in an equivariant stable cohomotopy group refining the Seiberg-Witten invariant. This first of two articles presents the details of the definition of the stable cohomotopy invariant and discusses its…

A deformation of the canonical algebra for kinematical observables of the quantum field theory in Minkowski space-time has been considered under the condition of Lorentz invariance. A relativistic invariant algebra obtained depends on…

\emph{Scalable spaces} are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat) differential forms. This is a rational homotopy invariant property and all scalable spaces are…

We build a bridge between geometric group theory and topological dynamical systems by establishing a dictionary between coarse equivalence and continuous orbit equivalence. As an application, we give conceptual explanations for previous…

We demonstrate that all perturbative scale invariant heterotic sigma models with a compact target space $M^D$ are conformally invariant. The proof, presented in detail for up to and including two loops, utilises a geometric analogue of the…

We consider finite point subsets (distributions) in compact metric spaces. In the case of general rectifiable metric spaces, non-trivial bounds for sums of distances between points of distributions and for discrepancies of distributions in…

We find an extension of the quasi-metric (to be called $g$-quasi metric) such that the induced generalized topology may fail to form a topology. We show that $g$-quasi metrizability is a $g$-topologically invariant property of generalized…

In this paper, first we prove the existence of invariant vector field on a homogeneous Finsler space with infinite series $(\alpha, \beta)$-metric and exponential metric. Next, we deduce an explicit formula for the the $S$-curvature of…

We give precise estimates of some holomorphically invariant infinitesimal metrics near a pseudoconcave points in a wide family of ``model'' domains for that situation in $\mathbb C^2$. This extends to metrics (rather distances) the authors'…

Various definitions of chiral observables in a given Moebius covariant two-dimensional theory are shown to be equivalent. Their representation theory in the vacuum Hilbert space of the 2D theory is studied. It shares the general…

We define a new finite type invariant for stably homeomorphic class of curves on compact oriented surfaces without boundaries and extend to a regular homotopy invariant for spherical curves.

Magnitude is a numerical invariant of finite metric spaces, recently introduced by T. Leinster, which is analogous in precise senses to the cardinality of finite sets or the Euler characteristic of topological spaces. It has been extended…

The conformally invariant symmetric traceless field $A$ is considered. In four dimensions it possesses a scalar gauge invariance to which we provide a conformally invariant gauge fixing equation. A field strength $F$ is built upon $A$, its…

Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the…

Motivated by recently explored examples, we undertake a systematic study of conformal invariance in one-dimensional sigma models where an isometry group has been gauged. Perhaps surprisingly, we uncover classes of sigma models which are…

We present some old and new results on a class of invariant spaces of holomorphic functions on symmetric domains, both in their circular bounded realizations and in their unbounded realizations as Siegel domains of type II. These spaces…